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length of the unknown sides. What is the area of the figure? Show your work. ? JP4 z ++ W ×12 984 4ft 90 3 ft 2 ft 9 ft 2 7 ft 12ft

length of the unknown sides. What is the area of the figure? Show your work. ? JP4 z ++ W ×12 984 4ft 90 3 ft 2 ft 9 ft 2 7 ft 12ft

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Find the length of the unknown sides. What is the area of the figures? Please show the work on how you solved the second question.
### Finding the Area of a Composite Figure #### Problem Statement Determine the length of the unknown sides. What is the area of the figure? Show your work. #### Explanation The image shows a composite figure consisting of two rectangles joined together. Let’s break down the problem step-by-step: 1. **Dimensions Provided:** - **Rectangle 1:** - Height: 3 ft - Width: 2 ft - **Rectangle 2:** - Height: 9 ft - Width: 7 ft 2. **Composite Figure:** - The entire structure is formed by connecting the two rectangles horizontally. 3. **Solve for Unknown Dimensions:** - The unknown lengths are the remaining sides of the rectangles after alignment. - From left to right: - Total Height = Height of Rectangle 1 (3 ft) + Height of Rectangle 2 (9 ft) = 12 ft. - Width of unknown top side = Total Width - Width of Rectangle 1 = 7 ft - 2 ft = 5 ft. - Height of unknown bottom side = Total Height - Height of Rectangle 2 = 12 ft - 9 ft = 3 ft. 4. **Calculating the Area:** - Area of Rectangle 1 = Height × Width = 3 ft × 2 ft = 6 sq ft - Area of Rectangle 2 = Height × Width = 9 ft × 7 ft = 63 sq ft - Total Area = Area of Rectangle 1 + Area of Rectangle 2 = 6 sq ft + 63 sq ft = 69 sq ft ### Conclusion The total area of the figure is 69 square feet.
Transcribed Image Text:### Finding the Area of a Composite Figure #### Problem Statement Determine the length of the unknown sides. What is the area of the figure? Show your work. #### Explanation The image shows a composite figure consisting of two rectangles joined together. Let’s break down the problem step-by-step: 1. **Dimensions Provided:** - **Rectangle 1:** - Height: 3 ft - Width: 2 ft - **Rectangle 2:** - Height: 9 ft - Width: 7 ft 2. **Composite Figure:** - The entire structure is formed by connecting the two rectangles horizontally. 3. **Solve for Unknown Dimensions:** - The unknown lengths are the remaining sides of the rectangles after alignment. - From left to right: - Total Height = Height of Rectangle 1 (3 ft) + Height of Rectangle 2 (9 ft) = 12 ft. - Width of unknown top side = Total Width - Width of Rectangle 1 = 7 ft - 2 ft = 5 ft. - Height of unknown bottom side = Total Height - Height of Rectangle 2 = 12 ft - 9 ft = 3 ft. 4. **Calculating the Area:** - Area of Rectangle 1 = Height × Width = 3 ft × 2 ft = 6 sq ft - Area of Rectangle 2 = Height × Width = 9 ft × 7 ft = 63 sq ft - Total Area = Area of Rectangle 1 + Area of Rectangle 2 = 6 sq ft + 63 sq ft = 69 sq ft ### Conclusion The total area of the figure is 69 square feet.
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